16 Teams meet each other 2 times, how many matchen are therw

To determine the total number of matches when 16 teams each play against every other team twice, follow these steps:

1. **Calculate the number of unique matches between teams**: Each pair of teams will play 2 matches. The number of unique pairs of teams from 16 teams is given by the combination formula \( \binom{n}{2} \):
   \[
   \binom{16}{2} = \frac{16 \times 15}{2} = 120
   \]

2. **Multiply by 2** to account for each pair playing twice:
   \[
   120 \times 2 = 240
   \]

So, there are **240 matches**.

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. How would the number of matches change if each pair of teams played only once?
2. What is the formula for combinations and how is it derived?
3. If 20 teams each play against every other team twice, how many matches will there be?
4. How does the number of matches scale with the number of teams?
5. Can you generalize this to other sports tournament structures?

**Tip**: When calculating combinations, the order of selection does not matter, which is why we use \( \binom{n}{2} \).

Learn how to calculate the total number of matches when 16 teams each play against every other team twice. This problem involves combinatorial mathematics and the combination formula. Suitable for high school students (Grades 10-12).

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